Probability for Primordial Black Holes in Multidimensional Universe with Nonlinear Scalar Curvature Terms

TL;DR

This paper explores the probability of primordial black hole formation in a multidimensional universe with nonlinear scalar curvature terms, using Euclidean instanton solutions in different topologies within a semiclassical framework.

Contribution

It introduces new gravitational instanton solutions in R^4-theory and evaluates their role in primordial black hole creation in multidimensional cosmological models.

Findings

Probability of black hole pair creation depends on topology and scalar curvature terms.

New instanton solutions in R^4-theory are relevant for cosmological models.

Quantum creation probability varies with cosmological constant and topology.

Abstract

We investigate multi-dimensional universe with nonlinear scalar curvature terms to evaluate the probability of creation of primordial black holes. For this we obtain Euclidean instanton solution in two different topologies: (a) $S^{D-1}$ - topology which does not accommodate primordial black holes and (b) $S^1\times S^{D-2}$-topology which accommodates a pair of black holes. The probability for quantum creation of an inflationary universe with a pair of black holes has been evaluated assuming a gravitational action which is described by a polynomial function of scalar curvature with or without a cosmological constant ($\Lambda $) using the framework of semiclassical approximation of Hartle-Hawking boundary conditions. We discuss here a class of new gravitational instantons solution in the $R^4$-theory which are relevant for cosmological model building.